Thermoelastic Modeling of Functionally Graded Media Incorporating Memory-Dependent Heat Conduction and Nonlocal Effects

Abstract This study presents a novel semi-analytical framework for modeling transient heat conduction in functionally graded longitudinal fins subjected to sudden thermal shock. The proposed approach addresses the limitations of classical Fourier and Cattaneo–Vernotte theories by integrating three advanced concepts into a single unified model: memory-dependent derivatives (MDD) with customizable kernel functions, fractional single-phase-lag (FSPL) non-Fourier conduction, and Eringen’s nonlocal elasticity. The framework captures memory effects, finite thermal wave speeds, and long-range microstructural interactions often overlooked in fractional models. Governing equations for a PSZ–SUS304 graded fin are solved in the Laplace domain with modified Bessel functions and inverted using Durbin’s method. Results indicate that stronger memory kernels delay thermal propagation, while nonlocal elasticity lowers peak stresses by 30–40% with modest efficiency loss. Validation against exact steady-state solutions for various material profiles confirms accuracy, with mean errors on the order of 10–8. The novelty lies in coupling memory‑dependent derivatives, fractional single‑phase‑lag conduction, and nonlocal elasticity to simultaneously capture history effects, finite wave speeds, and microstructural interactions beyond classical models.